Wyo. Stat. § 20-2-102
When the husband and wife are living separately, or when they are living together but one (1) spouse does not support the other spouse or children within his means, and no proceeding for divorce is pending, the other spouse or the department of family services may institute a proceeding for support. No less than five (5) days after notice is personally served upon the nonsupporting spouse, the court may hear the petition and grant such order concerning the support of the spouse or children as it might grant were it based on a proceeding for divorce. If the nonsupporting spouse cannot be personally served within this state but has property within the jurisdiction of the court, or debts owing to him, the court may order such constructive service as appears sufficient and proper and may cause an attachment of the property. Upon completion of constructive service the court may grant relief as if personal service was had.
W.S. 20-2-102